In Safari for iPhone and iPad you can run bookmarklets from the bookmark menu. If you try that in Chrome for iOS you get an error saying that the URI scheme is not supported.
It is possible to run bookmarklets in Google Chrome but the way to do it is less than obvious. Here's how you do:
Write the name of the bookmarklet in Chromes address/search field. As you start writing you will see that at the bottom of the list of matches there are entries with a star to the left. Those are bookmarks and bookmarklets. Tap the one you want to run.